In: Statistics and Probability
Suppose you sample 19 high school baseball pitchers and find that they have an average pitching speed of 87 miles per hour with a standard deviation of 0.98 mph. Find a 95% confidence interval for the average pitching speed of all high school baseball pitchers. Assume that the population is normally distributed.
Solution :
sample size = n = 19
Degrees of freedom = df = n - 1 = 18
t /2,df = 2.101
Margin of error = E = t/2,df * (s /n)
= 2.101 * (0.98 / 19)
Margin of error = E = 0.5
The 95% confidence interval estimate of the population mean is,
- E < < + E
87 - 0.5 < < 87 + 0.5
86.5 < < 87.5
(86.5, 87.5)